Performance of machine learning algorithms in spectroscopic ellipsometry data analysis of ZnTiO3 nanocomposite

In this research, the optical properties of the PVP: ZnTiO3 nanocomposite are studied using the spectroscopic ellipsometry technique. The preparation procedure of the ZnTiO3 nanocomposite is explained in detail. The absorbance/transmittance, surface morphology, structural information, chemical identification, and surface topography of the ZnTiO3 nanocomposite is studied using UV–Vis spectroscopy, field-emission scanning electron microscopy, Raman spectroscopy, Fourier transform infra-red, and atomic force microscopy, respectively. The ellipsometry method is used to obtain the spectra of the real and imaginary parts of the dielectric function and refractive index in the photon energy range of 0.59–4.59 eV. Moreover, using two machine learning algorithms, namely artificial neural network and support vector regression methods, the ellipsometric parameters ψ and Δ are analyzed and compared with non-linear regression. The error and accuracy of each three methods, as well as the time required for their execution, are calculated to compare their suitability in the ellipsometric data analysis. Also, the absorption coefficient was used to determine the band gap energy of the ZnTiO3 nanocomposite, which is found to be 3.83 eV. The second-energy derivative of the dielectric function is utilized to identify six critical point energies of the prepared sample. Finally, the spectral-dependent optical loss function and optical conductivity of the ZnTiO3 nanocomposite are investigated.


Synthesis of ZnTiO 3 nanostructures and preparation of its composite
The precursors of TiCl 4 (≥ 99%) and Zn(CH 3 COO) 2 .2H 2 O (≥ 99%) have been furnished by ROYALEX and Merck Companies, respectively.The details of procurement procedures of TiO 2 nanostructures have been introduced in Ref. 38 .To provide TiO 2 nanostructures, 20 cc of NaOH (0.2 M) was dropwise added to 22 cc of TiCl 4 in the liquid phase on a magnetic stirrer, and after evaluating the pH of the mixture, it was irradiated by microwaves at 800W for 10 min.The distilled water was employed to wash the resulting white mixture before drying at 25 °C.For synthesizing the ZnTiO 3 nano-powders, three separate beakers of Zn(CH 3 CO 2 ) 2 (0.2 M), NaOH (0.2 M), and TiO 2 (0.15 M) solutions were initially made ready.Next, the solutions of TiO 2 and NaOH were dropwise added to Zn(CH 3 CO 2 ) 2 solution at a temperature of 25 °C under ultrasonic irradiation.The product was placed in a microwave device and exposed to 800 W microwave radiation for 10 min.Then, the result was dried at the 25 °C temperature after rinsing during centrifugation.Eventually, the resulting nano-powder was annealed at the 700 °C temperature for 2 h.The preparation procedure of the ZnTiO 3 nanostructures is schematically shown in Fig. 1.
It should be noted that a p-type Si wafer with a 300 µm thickness was employed as a substrate in this research.To prepare PVP: ZnTiO 3 interfacial polymer layer, 10 mg of ZnTiO 3 nanostructures was dispersed by ultrasonic technique after providing a 5% solution of PVP with solvating 5 g of PVP nano-powders in 95 cc water.Then, a thin layer of PVP: ZnTiO 3 with a thickness of 100 nm was deposited on the Si wafer using a spin coater system.

UV-Vis spectroscopy
The UV-Vis spectroscopy was performed by Shimadzu UV-1800 in the wavelength range of 200-800 nm to determine the absorbance and transmittance of the ZnTiO 3 nanocomposite (see Fig. 2a).As can be seen, the absorbance of the ZnTiO 3 nanocomposite is decreased by raising the wavelength while the transmittance increases.In addition, Tauc's equation is used to determine the optical band gap of the ZnTiO 3 nanocomposite which is equal to 3.87 eV (see Fig. 2b) 38 .

SEM Image
The scanning electron microscope (SEM) (model LEO 1430 VP) at 15 kV accelerator voltage was utilized to record the SEM images to survey the morphology of the ZnTiO 3 nanocomposite.The surface-morphology schema of the prepared ZnTiO 3 nanocomposite is depicted in Fig. 3.Because of the difficulty of observing the sizes of actual particles, the structure of polydispersity nanoparticles appears in various configurations with an average size of ˂50 nm.Furthermore, all nanoparticles are clustered to form micron-sized clusters.

Raman spectroscopy
A potent analytical method established on the inelastic scattering of light is Raman spectroscopy, enabling unmatched structural information on the atomic scale.A high-resolution Raman spectrometer system (inno-Ram™) was used in this research to record the Raman spectrum of the ZnTiO 3 nanocomposite.Based on the prediction of group theory (point group C3i), 10 Raman active modes are assigned to the ZnTiO 3 , i.e., 5A g + 5E g 39 .
Figure 4 shows the Raman spectrum of ZnTiO 3 nanocomposite in the Raman shift of 140-800 cm −1 .The Raman vibrations of the ZnTiO 3 molecule were observed at the Raman shift of 152, 190, 225, 265, 346, 384, 477, 494,  619, and 724 cm −1 corresponded to the symmetrical phonon modes of E g , A g , E g , A g , A g , E g , E g , A g , E g , and A g , respectively.These peaks confirm the presence of ZnTiO 3 nanostructure in the prepared PVP: ZnTiO 3 nanocomposite.However, the observation of noise in the Raman spectrum is due to the composite of the thin layer.It is necessary to mention that low-frequency vibration modes only appeared for the particles or crystallites at nanometric size 40    Figure 5 represents the ATR and FTIR spectra of PVP: ZnTiO 3 nanocomposite with the assignment of the primary ATR and FTIR bands.Since the distinctive bands of metal oxides (< 750 cm −1 ) correspond to the bonds between metal and oxygen, the absorption band at the wavenumber range of 600-1000 cm −1 is attributed to the Ti-O, O-Ti-O, Zn-O, O-Zn-O, and Zn-Ti-O linked to ZnTiO 3 species (see Fig. 5a).In more detail, the Ti-O bond vibrations are observed at the low wavenumber region from 400 to 650 cm −141 .The Zn-Ti-O vibration modes were detected at 735 cm −1 .Moreover, the Ti-O octahedral absorption band appears at the wavenumber of 560 and 590 cm −1 .The bands at the wavenumber of 550-650 cm −1 are assigned to TiO 6 vibration modes 42 .
It is obvious that the bands at higher wavenumber regions are related to the CH 2 symmetric bending vibration, C-H asymmetric stretching vibration, and O-H stretching vibration corresponding to 2922, 2955, and 3496 cm −1 , respectively.It should be mentioned that the PVP is a macropolymer with CH 2 , C=O, and C-N functional groups, consisting of a very hydrophilic part and large hydrophobic groups.Since water and several non-aqueous liquids are supreme solvents for PVP, water has been used to solve the PVP polymer nano-powder in this work and hence, the O-H group appears in the FTIR spectrum (see Fig. 5b) 35 .

Atomic force microscopy (AFM) image
The spectroscopic ellipsometry (SE) method is based on measuring the polarization of light after reflecting from a surface.It is generally accepted that optical elements do not depolarize light.However, there are certain circumstances where this assumption may not hold and depolarization can occur.For instance, when the light illuminates an area of the sample surface where the film thickness is non-uniform, it can lead to quasi-depolarization.Moreover, some of the light that reaches the polarization state detector may not have a distinguishable polarization state or cross-polarization may occur in systems that are theoretically isotropic if the sample is highly rough.On the other hand, atomic force microscopy (AFM) is an appropriate method to determine the surface roughness.
AFM, a form of scanning probe microscopy (SPM), has exhibited a resolution with an order of a nanometer compared to the optical diffraction limit.AFM uses the feeling of touching the surface with a mechanical probe to get the data.Piezoelectric components allow for small, exact movements under (electrical) control, enabling perfect scanning.It is possible to create a high-resolution image of the topography of a sample surface using the probe's response to the forces the sample imposes on it.In this work, an atomic force microscope (model WITec alpha300 A) has been employed to record the 3-dimensional shape of the surface of the PVP: ZnTiO 3 thin film.The topography of the ZnTiO 3 nanocomposite recorded by the AFM is represented in Fig. 6.As shown, since the ZnTiO 3 nanocomposite's surface roughness is ⁓ 1.05 nm, this nanocomposite thin film is smooth in the sub-nanometer scale.

Spectroscopic ellipsometry (SE) method spectroscopy
The Spectroscopic Ellipsometry (SE) technique is typically a non-invasive, non-destructive measurement method that uses reflected light waves to determine a sample material's optical properties.The SE method does not require absolute intensity as long as the absolute intensity is sufficient because it assesses a relative change in polarization.The SE measurement is exceedingly accurate and repeatable as a result 43 .
Ellipsometry makes use of the fact that linearly polarized light at an oblique incidence to a surface changes its polarization state when reflected.It is elliptically polarized, giving rise to the term "ellipsometry".In addition, the incident light wave might be elliptically polarized light in some circumstances.Figure 7 depicts the general concept of ellipsometry.
Once a monochromatic plane light wave is obliquely incident on a surface, the plane of incidence is defined as a plane perpendicular to the surface, including the vector pointing in the light wave's propagation direction 44 .This vector is referred to as the wavevector k in .The two mutually perpendicular vectors of the light wave's electric field E and magnetic field B are perpendicular to k in .The only vector displayed in Fig. 7 is the E-vector, which is selected to represent the polarization of the light wave.The E-vector is divided into two parts that are perpendicular to each other and perpendicular to k in 44 .Figure 7 shows how the two components of E are parallel and perpendicular to the plane of incidence.As observed, the ellipsometer used in this work consists of seven optical elements (1) light source, (2) light collimator, (3) polarizer, (4) sample (ZnTiO 3 nanocomposite), ( 5) phot-elastic modulator (PEM), ( 6) analyzer, and ( 7) detector.
The light wave that is incident to the surface is linearly polarized.The p-and s-components of the E field can be considered as oscillating with a specific amplitude and mutual phase whose endpoint moves in a straight line on the plane of p-and s-components 43 .The polarization of the light wave changes to an elliptical state after reflecting off the surface.As a result of the amplitude and mutual phase of the p-and s-components of E field changing, the endpoint of E moves in an ellipse.A detector can measure the ellipse's shape that is related to the ellipsometric parameters ψ and Δ by data processing.It should be mentioned that HORIBA (JOBIN YVON UVISEL 2) spectroscopic ellipsometer has been utilized in this work to get the ellipsometric parameters at the fixed incidence angle of 70° in room temperature.The ellipsometric parameters can be connected to the reflection coefficients of light polarized parallel and perpendicular to the plane of incidence 43 .
Figure 8 illustrates the variations in the ellipsometric parameters (ψ and Δ) within the photon energy range of 0.59-4.59eV.The experimental measurements of ψ and Δ have been analyzed not only through the NLR fitting process but also through the application of two ML algorithms, namely the ANN and SVR algorithms.As the figure shows, the fitting values are very close to the experimental ones.
To compare the obtained results more accurately, the R2 score criterion has been calculated separately for the mentioned methods.The R2 score essentially indicates the accuracy of the performed calculations, and the closer it is to the value of one, the more it signifies that the parameters considered in the algorithms were appropriate and the training was more comprehensive; Consequently, the mean deviation between the fitted values and the actual values is less.Moreover, the mean absolute error (MAE) is the other essential parameter in determining the accuracy of the analysis methods applied in this work.Table 1 introduces the value of the R2 score, MAE,

Substrate
Nanocomposite Layer www.nature.com/scientificreports/and time needed to execute each of the applied algorithms for analyzing the ellipsometric parameters.The values of MAE and R2 score for the SVR algorithm are lower and higher than other algorithms in the analysis process, respectively.The time spent in ML algorithms for analyzing both ψ and Δ is lower than NLR.Moreover, the time spent in SVR is significantly lower compared to the other two algorithms.

Results and discussion
The materials can be optically characterized via ellipsometric techniques.After illuminating the sample with a linearly polarized light beam, the reflected light is collected.To obtain the ellipsometric data, the amplitude ratio (ψ) of the parallel (p) and perpendicular (s) components of the reflected light, as well as the phase difference between them should be measured.The complex reflectance ratio (ρ) of the polarized light relates to the ψ and Δ ellipsometric parameters as 45 : with r p and r s being Fresnel reflection coefficients of the reflected polarized light.The air-sample optical model to obtain the dielectric function is given by 45 ; where φ denotes the angle of incidence, ε 0 is the dielectric constant of air, and ε 1 and ε 2 refer to the real and imaginary parts of dielectric constants, respectively.Figure 9 represents changes of ɛ 1 and ɛ 2 parts of the complex dielectric function acquired by the analysis of ellipsometric data based on the air-sample optical model.There is a maximum in the spectrum of ɛ 1 at the photon energy of 3.24 eV.Moreover, a significant decreasing point is observed at photon energy 2 eV.Similar ɛ 2 -spectrum behavior has previously been reported in numerous ellipsometry measurements on diverse samples [46][47][48][49][50][51] .There are two peaks in the ɛ 2 -spectrum at 3.39 eV and 4.24 eV which are attributed to inter-band transitions or critical points (CPs).Spectral-dependent refractive index (n) and extinction coefficient (k) are defined by using the spectra of ɛ 1 and ɛ 2 as follows 52 :  A peak in the extinction coefficient spectrum has appeared at the same energy position of the ɛ 2 -spectrum.The band gap energy of the ZnTiO 3 nanocomposite was calculated to be 3.83 eV which is in good agreement with the E g values of 3.87 eV and 3.80 eV respectively introduced in refs. 6,53.It can be observed that the value of the extinction coefficient is decreased at energies lower than the band gap energy.Additionally, the refractive index of the ZnTiO 3 nanocomposite is 3.24 at the band gap energy (⁓3.87 eV), and it changes between 3.16 and 4.15 at the visible spectral region, i.e., 1.77-3.26eV.Based on the changes of ε 2 (ω), the electron transitions from valence bands to conduction bands are what cause the peaks in the extinction and absorption coefficients (see Figs. 10, 11a).After obtaining the refractive index and extinction coefficient of the ZnTiO 3 nanocomposite, the absorption coefficient α(E) and orthogonal incident reflectance R(E) could be derived as 54 : (3) www.nature.com/scientificreports/It must be noted that SE measurements on any other faces besides the crystal's usual layer-plane face are extremely challenging due to the crystal's layer organization.It is appropriate to investigate the current SE measurement spectra using the binary phase (air/sample) instance.The spectral dependencies of the absorption coefficient (α) and the reflectance coefficient are introduced in Fig. 11a.The absorption spectrum has a peak and a local maximum the wavelength of 282 nm and 360 nm, respectively.The absorption coefficient is generally declined by increasing the wavelength and is zero in the wavelength range of 1000-1100 nm.A similar behavior could be seen in the reflectance spectrum except for zero value at no wavelength.Furthermore, the absorption coefficient and band gap energy could be related to each other as follows 55 : where m refers to a constant value which is 2 and 0.5 for indirect and direct transitions, respectively.Based on Eq. ( 7), if (αhv) 1/m is plotted as a function of hv at the absorption edge region, the band gap energy (E g ) could be determined by the point where the fitted straight line intersects the energy axis.As can be seen from Fig. 11b, the indirect band gap energy for the ZnTiO 3 nanocomposite equals 3.83 eV, where fitted straight line intersects the energy axis.This E g is in good agreement with the reported E g values for ZnTiO 3 nanocomposite 53 .These results were confirmed by the UV-Vis spectroscopy presented in Sect.2.2.According to Ref. 45 , interband transition energies (also known as critical points, or CPs) could be examined by analysis of second-energy derivatives of different dielectric function components.Theoretically, the critical point energy (E cp ), photon energy (E), broadening parameter (Γ), amplitude (A), and phase angle (φ) relate to the second-energy derivative spectra of the components of the dielectric function as 45 : where m refers to the dimensions of the wave vectors involved in optical transitions.For excitonic, one, two, and three-dimensional lineshapes, the m values are 1, 1/2, 0, and + 1/2, respectively.The second-energy derivative spectra of ε 1 (circles) and ε 2 (stars) components are shown in Fig. 12.In the energy region, where the smoothing method has no effect on the main and first derivative spectra, a fitting process was used.As can be seen from Fig. 12, the fitting approach was used in this energy range because dielectric function components exhibit notable changes outside the 2.5-4.5 eV range.
The fitting applications had the lowest mean square deviations in the case of excitonic optical transitions (corresponding to m = -1).Six CP energies of 3.39, 3.72, 3.89, 4.09, 4.24, and 4.44 eV were obtained by fitting experimental data to theoretical definitions in the considered energy range.Near to CP energies are the observed ( 5) www.nature.com/scientificreports/local and absolute maximum values in the ε 2 spectrum.These CP energies show that the sample can absorb photons with these energies.For additional analysis, the Wemple and DiDomenico single effective model and the Spitzer-Fan model have been used to examine the refractive index and real component of the dielectric function spectra.If the photon energy is lower than the band gap energy (hv < g ), the refractive index could be expressed as follows using the Wemple and DiDomenico 56 : with E d and E so being the energy and single oscillator energy, respectively.E so is described as the average band gap energy, whereas E d corresponds to the intensity of the interband optical transition.To obtain the E d and E so values, the graph of (n 2 -1) −1 should be plotted as a function of (hv) 2 as shown in Fig. 13a.The slope and the intercept of the linear fit are applied for calculating the value of E d and E so energies equal to 33.1 and 4.43 eV, respectively.Moreover, the value of the refractive index (n 0 ) and dielectric constant (ε 0 ) at zero frequency (v = 0) could be computed by using definitions of n 0 = (1 + E d /E so ) −1 and ε 0 = n 2 0 as 2.41 and 8.47, respectively.The wavelength-dependent real part of the dielectric function (ɛ 1 ) is given by the Spitzer-Fan model as 57 (10) where ε ∞ refers to the dielectric constant at high frequencies, N denotes the carrier concentration, m* symbolizes the effective mass, c and e are the speed of light and electron charge.When n 2 -k 2 is plotted in terms of λ 2 (see Fig. 13b), the slope and intercept of the linear fit are used to compute the values of ε ∞ and N/m* found as 19.7 and 3.7 × 10 53 kg −1 cm −3 , respectively.Finally, it is useful to study the optical loss function, L(ω), and optical conductivity, σ(ω), which are defined using the dielectric function, ε(ω), as [58][59][60] : Figure 14a represents the loss function of the ZnTiO 3 nanocomposite.Generally, the energy-loss function, whose absolute maximum and matching frequencies are related to the plasma oscillations and the plasma frequency, depicts the energy loss when a fast electron in a material and deflects its route.As seen, the loss function of the ZnTiO nanocomposite has no absolute in the considered photon energy although there is an absolute minimum at the photon energy of 1.15 eV. Figure 14b reveals the spectral dependencies of the optical conductivity of the ZnTiO 3 nanocomposite in the considered photon energy.Optical conductivity consists of two components, i.e., σ 1 (ω) and σ 2 (ω), which are directly related to photocurrent and photoresistance 61,62 .As expected, the behavior of real and imaginary components of the optical conductivity and dielectric function are opposite.So, the ε 2 (ω) directly gives the σ 1 (ω) that indicates the absorption or energy loss in a material caused by light-induced electric current.The absorption or energy loss in the ZnTiO 3 nanocomposite increases with the increment of the photon energy till 4.4 eV, and it reduces after that.However, a relative reduction is observed in the absorption/loss after the photon energy of 3.45 eV.The inter-band transition between unoccupied and occupied states is the main reason for the appearance of the peaks in the σ 1 (ω) spectra.On the other hand, the σ 2 (ω) is obtained by the ε 1 (ω), and it demonstrates the energy storage capacity of a material that is directly relevant photoresistance.Therefore, the profile of the imaginary part of optical conductivity, σ 2 (ω), shows that the energy storage capacity in the ZnTiO 3 nanocomposite is minimum at the photon energy of 3.4 eV.

Conclusion
In this work, the spectroscopic ellipsometry method was employed to measure the optical properties of the PVP: ZnTiO 3 nanocomposite.The details of the preparation process of the ZnTiO 3 nanocomposite were described.UV-Vis spectroscopy, Field-Emission Scanning Electron Microscopy (FESEM), Raman spectroscopy, Attenuated Total Reflectance (ATR)-Fourier transform Infra-Red (FTIR), and Atomic Force Microscopy (AFM) were used to study the absorbance/transmittance, the surface morphology, structural information, chemical identification, and surface topography of the ZnTiO 3 nanocomposite, respectively.The energy of the optical band gap was calculated to be 3.87 eV.It was observed that the average size of the polydispersity nanostructures was less than 50 nm.According to the group theory prediction (5E g + 5A g ), ten Raman active modes of the ZnTiO 3 appeared in the Raman shift of 140-800 cm −1 .The vibration modes of Ti-O, Zn-Ti-O, and TiO 6 were detected at the low wavenumber region 400-650 cm −1 .The functional groups of CH 2 , C-H, and O-H were also observed at the wavenumber region of 2000-3700 cm −1 , relating to the PVP polymer and water molecules used as a solution in the preparing process of PVP: ZnTiO 3 nanocomposite.Moreover, the roughness of the ZnTiO 3 nanocomposite surface was ⁓ 1.05 nm, meaning the considered nanocomposite is smooth on the sub-nanometer scale.
The ellipsometric parameters (ψ and Δ) that were experimentally measured, were analyzed by the common NLR method and two algorithms of ML technique, i.e., ANN and SVR.This was done to demonstrate the efficiency of ML algorithms in ellipsometry data analysis.The obtained results show that the accuracy of data analysis using NLR, ANN, and SVR methods is very high and significant.Also, the values of the MAE and R2 score of the SVR algorithm are lower and higher than both other methods, respectively.On the other hand, the time required to analyze the ellipsometric data was calculated for all three methods.The comparison shows that the NLR method is time-consuming concerning the ANN and SVR methods.Moreover, the time needed for SVR is much less compared to the other two methods.Therefore, it can be concluded that ML algorithms can be a suitable alternative for ellipsometric data analysis, and the SVR method is preferred to the ANN method due to its low MAE, more accuracy, and less time consumption.
In addition, the spectral-dependent real and imaginary parts of the function (ε = ε 1 + iε 2 ) and refractive index (N = n + ik) were measured by the ellipsometry method at the photon energy range of 0.59-4.59eV.The energydependent absorption and reflectance coefficients of the ZnTiO 3 nanocomposite were obtained.It was found that the peaks that appeared in the absorption and extinction coefficients were due to the electron transitions from valence bands to conduction bands.Furthermore, the band gap energy of the ZnTiO 3 nanocomposite was computed as 3.83 eV using the absorption coefficient spectrum.The second-energy derivative of the dielectric function was applied to find the six critical point energies of the prepared sample in the energy range of 2.5-4.5 eV, indicating the sample can absorb photons at these energies.Based on the Wemple and DiDomenico model, the zero-frequency refractive index (n 0 ) and dielectric constant (ε 0 ) of the considered sample were calculated as 2.41 and 8.47, respectively.The high-frequency dielectric constant (ε ∞ ) was obtained by the Spitzer-Fan model, equal to 19.7.At last, the spectral dependencies of the optical loss function and the optical conductivity of the ZnTiO 3 nanocomposite were studied.

Figure 9 .Figure 10 .
Figure 9.The energy-dependent (a) ε 1 and (b) ε 2 components of the dielectric function of ZnTiO 3 nanocomposite determined by SVR and ANN inferences and by nonlinear regression (manual fitting regression).

Figure 12 .Figure 13 .
Figure 12.Second-derivative of the real and imaginary parts of dielectric function in terms of photon energy.Solid lines are the best fit.

Attenuated total reflectance (ATR) & Fourier transform infra-red (FTIR) spectroscopy ATR
and FTIR spectroscopy methods are commonly applied for investigating the chemical identification of a desired sample.The ATR and FTIR spectra have been measured by BRUKER (vertex 80) device in this work.

Table 1 .
The NLR, ANN, and SVR algorithms time to model in predicting the ellipsometric angles ψ and Δ.